given that x+y=1, prove that 1/x + 1/y >= 4
Appreciate any help/hints!
you also need to have x > 0 and y > 0. first note that from $\displaystyle (t-1)^2 \geq 0,$ we get: $\displaystyle t + \frac{1}{t} \geq 2,$ for any $\displaystyle t > 0.$ thus: $\displaystyle \frac{1}{x} + \frac{1}{y} = (x+y) \left(\frac{1}{x} + \frac{1}{y} \right)=2 + \frac{x}{y} + \frac{y}{x} \geq 4.$